Piltdown

Are cases like the Piltdown hoax rare in science?
If by rare you mean the frequency by which deliberate hoaxes are perpetrated in order to promote a scientific theory then yes, cases like the Piltdown hoax are relatively rare, though they do happen occasionally. Archaeoraptor is a more recent example of another case in which fossils were doctored to promote Darwinian evolution.

If you are referring to the frequency by which conclusions are falsely drawn from information (whether the information is deliberately falsified or not) then the answer is no, it is not rare at all. It happens fairly often. Scientists are constantly revising the “facts” as they see them, thereby affirming that the previous conclusions drawn from the evidence were false.

The Nebraska Man is a classic example of this. Though not a deliberate hoax like the Piltdown Man, whereby someone deliberately falsified evidence, Nebraska Man was simply a case of mistaken identity. An extinct pig’s tooth was found and misinterpreted to belong to some kind of ape-man. This misclassification stood for almost a decade before it was refuted.
The moral of the story is: scientists are not omniscient. We are all prone to delusion, even those of us trained to discern the truth. There are usually competing interpretations of evidence to be considered and presuppositions to be weighed. A well-rounded person is one who knows the various perspectives, knows the pros and cons, knows what they believe, and knows why they believe it.